Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with a = 3.1%. A random sample of 10 bank stocks gave the following yields (in percents). 5.7 4.8 6.0 4.9 4.0 3.4 6.5 7.1 5.3 6.1 The sample mean is x = 5.38%. Suppose that for the entire stock market, the mean dividend yield is u = 4.2%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.2%? Use a = 0.01. (a) What is the level of significance? .01 State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? O H: = 4.2%; H,: u # 4.2%; two-tailed H,: = 4.2%; H,A > 4.2%; right-tailed O H,: H = 4.2%; H,: u < 4.2%; left-tailed O H,: H > 4.2%; H,: µ = 4.2%; right-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since we assume that x has a normal distribution with unknown a. O The Student's t, since n is large with unknown a. O The standard normal, since we assume that x has a normal distribution with known a. O The Student's t, since we assume that x has a normal distribution with known o. Compute the z value of the sample test statistic. (Round your answer to two decimal places.) 1.17 (c) Find (or estimate) the P-value. (Round your answer to four decimal places.) 1210
Optimization
Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.
Integration
Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.
Application of Integration
In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.
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In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).
Area
Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.
Given information
Sample mean x̅ = 5.38%
Population mean µ = 4.2%
Sample size = 10
Standard deviation σ = 3.1%
Significance level (α) = 0.01
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